4 problems

Hyperbolicity-preservation conjecture. The operator

Consider the sequence … A pair $(b,c)$ lies in the multiplier sequence region when this sequence is a multiplier sequence for the Legendre basis. Quartic Legendre multiplier sequen…

Monotonicity conjecture. If $T$ is not monotone, then $T$ is not hyperbolicity preserving.

Let $T$ be a constant-coefficient difference operator … It acts on hyperbolic polynomials of degree at most $m$ whose mesh is at least one, where the mesh is the minimum distance b…